need help with pre-calculus problems???

Question

any help is appreciated and some sort of explanation to go along with it!!!! thx!!!

1. Multiply three consecutive integers together and then add the second integer to that product. Use synthetic division to help prove that the sum is the cube of an integer, and determine which integer.

2. Flights of leaping animals typically have parabolic paths. The length of a frogs leap is 9 feet, the minimum height off the ground is 3 feet. Find a standard equation for the path of the frog.

3. A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet) of the outer ripple is r(t) = 0.6t, where t is the time in seconds after the pebble strikes the water. The area of the circle is given by the function A(r) = pie^2. Find and interpret (A or)(t).

Answer 1

2. I assume you meant maximum height. The zeros are 0 and 9 so the formula is h = a(x)(x-9)= ax^2 - 9ax

The maximum of 3 occurs when x = 4.5 (halfway from one end to the other, so 3 = a(4.5)^2 - 9a(4.5) . Solve this for a

Answer 2

1. For problems like these, you should go step by step as the proplem says:
a) The product of three consecutive integers:
let the first be x, the next will be x+1 and the third x+2
=x(x+1)(x+2)
=x(x^2+3x+2)
=X^3+3x^2+2x
b) Then add the second number which is (x+1)
=(x^3+2x^2+2x)+(x+1)
=x^3+3x^2+2x+x+1

c)When we substitute x= -1 into the previous equation we get an answer of 0. Therefore ( x+1) is factor. by Synthetic division:
we get (x+1)(X^2+2x+1)
by factorising we get: (x+1)(x+1)(x+1) which is equal to
(x+1)^3
Therefore (x+1)= second number

you can even try different values:
take :4,5 and 6 as three consecutive numbers:
Therefore:
4*5*6=120
120+5=125
and the cube root of 125 = 5 which is always the second number.

do the same for other questions as well

hope this is helpful
Roger

Answer 3

1) (n-1)*n(n+1) =(n^2-1)*n = n^3-n If you add n you get n^3 which is the cube of the middle number.Why to use syntetic division??
2) I suppose you are speaking of the "maximum" height off ground
If the frog is at x= 0 the other root is x=9

The standard equation would be a(x-9)*x =y

The vertix is at x= 4.5 (midpoint of the roots)
y(4.5) =a (-4.5)*(4.5) = 3 so a=-0.
The equation is y=-0.148*x*(x-9)
I'll leave the last to you

Answer 4

Not quite Pre-Calc

A * (A+1) * (A+2) +A+1
(A^2+A)*(A+2) + A +1
A^3 +2A^2 +A^2 +2A + A + 1
A^3 +3A^2 +3A + 1 = (X)^(-3)